Anomalous scaling at the quantum critical point in itinerant antiferromagnets

Quantum phase transitions (QPT) were investigated to show that the Hertz φ⁴ theory of quantum criticality is incomplete as it misses anomalous nonlocal contributions to the interaction vertices. The theory was found to be renormalizable for antiferromagnetic quantum transitions only if the dynamical exponent z=2. The Gaussian fixed point was found to split into two non-Gaussian fixed points for d<2. The results show that for both fixed points, the dynamical exponent remains z=2.